Felddistribution

Felddistribution, or field distribution, denotes how a physical field varies in space within a given region. It specifies the magnitude and direction of the field at each point and is central to problems in electromagnetism, optics, gravitation, and quantum mechanics.

Field distributions are described by scalar or vector fields, such as E(r) for electric field or B(r) for magnetic field, or by the probability amplitude in quantum contexts.

In static problems, field distributions satisfy governing equations and boundary conditions; for example, Maxwell's equations reduce to Laplace or Poisson equations in electrostatics. In dynamic cases, distributions evolve according to time-dependent field equations.

Common computational approaches include the finite element method, finite-difference time-domain method, and boundary-element method. In optics, the transverse field distribution in waveguides and resonators defines modes (e.g., Gaussian, Hermite-Gaussian, Laguerre-Gaussian) and determines propagation characteristics.

Applications span antenna design and radiation patterns, electromagnetic compatibility, optical fiber technology, near-field imaging, and the study of fields around structured materials or nanoscale devices.

Understanding field distribution also informs energy density and power flow via the Poynting vector, and helps predict interactions at interfaces and in heterogeneous media.

See also: Field theory, Maxwell's equations, Finite element method, Poynting vector, Mode analysis.